A Composite Initialization Method for Phase Retrieval

Phase retrieval is a classical inverse problem with respect to recovering a signal from a system of phaseless constraints. Many recently proposed methods for phase retrieval such as PhaseMax and gradient-descent algorithms enjoy benign theoretical guarantees on the condition that an elaborate estima...

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Autores principales:	Qi Luo, Shijian Lin, Hongxia Wang
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	phase retrieval spectral method non-convex reconstruction Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/bb37edc8b1b04cc9ac9f5a426c00aae8
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id	oai:doaj.org-article:bb37edc8b1b04cc9ac9f5a426c00aae8
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spelling	oai:doaj.org-article:bb37edc8b1b04cc9ac9f5a426c00aae82021-11-25T19:05:58ZA Composite Initialization Method for Phase Retrieval10.3390/sym131120062073-8994https://doaj.org/article/bb37edc8b1b04cc9ac9f5a426c00aae82021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2006https://doaj.org/toc/2073-8994Phase retrieval is a classical inverse problem with respect to recovering a signal from a system of phaseless constraints. Many recently proposed methods for phase retrieval such as PhaseMax and gradient-descent algorithms enjoy benign theoretical guarantees on the condition that an elaborate estimate of true solution is provided. Current initialization methods do not perform well when number of measurements are low, which deteriorates the success rate of current phase retrieval methods. We propose a new initialization method that can obtain an estimate of the original signal with uniformly higher accuracy which combines the advantages of the null vector method and maximal correlation method. The constructed spectral matrix for the proposed initialization method has a simple and symmetrical form. A lower error bound is proved theoretically as well as verified numerically.Qi LuoShijian LinHongxia WangMDPI AGarticlephase retrievalspectral methodnon-convex reconstructionMathematicsQA1-939ENSymmetry, Vol 13, Iss 2006, p 2006 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	phase retrieval spectral method non-convex reconstruction Mathematics QA1-939
spellingShingle	phase retrieval spectral method non-convex reconstruction Mathematics QA1-939 Qi Luo Shijian Lin Hongxia Wang A Composite Initialization Method for Phase Retrieval
description	Phase retrieval is a classical inverse problem with respect to recovering a signal from a system of phaseless constraints. Many recently proposed methods for phase retrieval such as PhaseMax and gradient-descent algorithms enjoy benign theoretical guarantees on the condition that an elaborate estimate of true solution is provided. Current initialization methods do not perform well when number of measurements are low, which deteriorates the success rate of current phase retrieval methods. We propose a new initialization method that can obtain an estimate of the original signal with uniformly higher accuracy which combines the advantages of the null vector method and maximal correlation method. The constructed spectral matrix for the proposed initialization method has a simple and symmetrical form. A lower error bound is proved theoretically as well as verified numerically.
format	article
author	Qi Luo Shijian Lin Hongxia Wang
author_facet	Qi Luo Shijian Lin Hongxia Wang
author_sort	Qi Luo
title	A Composite Initialization Method for Phase Retrieval
title_short	A Composite Initialization Method for Phase Retrieval
title_full	A Composite Initialization Method for Phase Retrieval
title_fullStr	A Composite Initialization Method for Phase Retrieval
title_full_unstemmed	A Composite Initialization Method for Phase Retrieval
title_sort	composite initialization method for phase retrieval
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/bb37edc8b1b04cc9ac9f5a426c00aae8
work_keys_str_mv	AT qiluo acompositeinitializationmethodforphaseretrieval AT shijianlin acompositeinitializationmethodforphaseretrieval AT hongxiawang acompositeinitializationmethodforphaseretrieval AT qiluo compositeinitializationmethodforphaseretrieval AT shijianlin compositeinitializationmethodforphaseretrieval AT hongxiawang compositeinitializationmethodforphaseretrieval
_version_	1718410301723901952

A Composite Initialization Method for Phase Retrieval

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